U^2+U=50

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Solution for U^2+U=50 equation: 


Simplifying
U2 + U = 50

Reorder the terms:
U + U2 = 50

Solving
U + U2 = 50

Solving for variable 'U'.

Reorder the terms:
-50 + U + U2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + U + U2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + U + 50 + U2 = 0 + 50

Reorder the terms:
-50 + 50 + U + U2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + U + U2 = 0 + 50
U + U2 = 0 + 50

Combine like terms: 0 + 50 = 50
U + U2 = 50

The U term is U.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
U + 0.25 + U2 = 50 + 0.25

Reorder the terms:
0.25 + U + U2 = 50 + 0.25

Combine like terms: 50 + 0.25 = 50.25
0.25 + U + U2 = 50.25

Factor a perfect square on the left side:
(U + 0.5)(U + 0.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(U + 0.5) equal to 7.088723439 and -7.088723439.


Subproblem 1
U + 0.5 = 7.088723439

Simplifying
U + 0.5 = 7.088723439

Reorder the terms:
0.5 + U = 7.088723439

Solving
0.5 + U = 7.088723439

Solving for variable 'U'.

Move all terms containing U to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + U = 7.088723439 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + U = 7.088723439 + -0.5
U = 7.088723439 + -0.5

Combine like terms: 7.088723439 + -0.5 = 6.588723439
U = 6.588723439

Simplifying
U = 6.588723439


Subproblem 2
U + 0.5 = -7.088723439

Simplifying
U + 0.5 = -7.088723439

Reorder the terms:
0.5 + U = -7.088723439

Solving
0.5 + U = -7.088723439

Solving for variable 'U'.

Move all terms containing U to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + U = -7.088723439 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + U = -7.088723439 + -0.5
U = -7.088723439 + -0.5

Combine like terms: -7.088723439 + -0.5 = -7.588723439
U = -7.588723439

Simplifying
U = -7.588723439


Solution
The solution to the problem is based on the solutions
from the subproblems.
U = {6.588723439, -7.588723439}

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